I need series-us help: Sum_(n=0)^inf(.7^n + .8^n) = 25/3

[Seed5813]

Sum_(n=0)^inf(.7^n + .8^n) = 25/3

I had to look up the answer but I can't find how to get it myself. The book only gives me a/(1-r) but there isnt a consistent ratio between the terms.

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[Steven G]

Sum_(n=0)^inf(.7^n + .8^n) = 25/3

I had to look up the answer but I can't find how to get it myself. The book only gives me a/(1-r) but there isnt a consistent ratio between the terms.

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Do you realize that the summation can be broken up into to two summation? What have you tried? If you show us what you tried we can guide you from there.

 

[Seed5813]

Do you realize that the summation can be broken up into to two summation? What have you tried? If you show us what you tried we can guide you from there.

All I tried was looking for a ratio and just adding up the first 13 terms. I didn't know i could split it

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[Steven G]

All I tried was looking for a ratio and just adding up the first 13 terms. I didn't know i could split it

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Assume for the moment that the summation is from 0 to 5 (instead of 0 to infinity). Then write out the 6 terms and see if you are able to separate the sum into two sums. Then we will go from there.

 

[Seed5813]

Assume for the moment that the summation is from 0 to 5 (instead of 0 to infinity). Then write out the 6 terms and see if you are able to separate the sum into two sums. Then we will go from there.

For sum_(n=0)^5(.7^n) i got 2.94117 and for sum_n=0^5(.8^n) I got 6.63045 which adds to 6.63045
And the same for the original front 0 to 5.

I guess I should try to find a ratio for the 2 sums?

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[Seed5813]

For sum_(n=0)^5(.7^n) i got 2.94117 and for sum_n=0^5(.8^n) I got 6.63045 which adds to 6.63045
And the same for the original front 0 to 5.

I guess I should try to find a ratio for the 2 sums?

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Which gives me 3.33... and 5 which adds to 8.333.... Thank you

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[Steven G]

For sum_(n=0)^5(.7^n) i got 2.94117 and for sum_n=0^5(.8^n) I got 6.63045 which adds to 6.63045
And the same for the original front 0 to 5.

I guess I should try to find a ratio for the 2 sums?

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Please write out the 6 terms. Then, if you can, separate the terms in a natural way.